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Category Time & Date

Date Input Select or enter a date

Or Enter Date Text ISO, US (MM/DD/YYYY), or EU (DD.MM.YYYY) format

Bit Width

Bit Grouping

Output Mode

Component-wise (Y/M/D) Unix Timestamp MS-DOS Packed Combined (YYYYMMDD)

Presets:

Select a date and click Convert to see binary representation

Bit Width Reference

Day (1-31): 5 bits minimum, typically stored in 8 bits

Month (1-12): 4 bits minimum, typically stored in 8 bits

Year (0-9999): 14 bits minimum, typically stored in 16 bits

Unix Timestamp: 32 bits (signed) or 64 bits for dates beyond 2038

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About

Date encoding in binary format serves critical functions in embedded systems, network protocols, and low-level data storage where memory efficiency determines system viability. The conversion process isolates each date component - year (Y), month (M), day (D) - and transforms them independently using positional notation with base 2. A year like 2024 requires 11 bits minimum (2¹¹ = 2048), while months fit in 4 bits and days in 5 bits. Miscalculating bit allocation causes overflow errors that corrupt downstream data - a 1-bit error in date storage propagates through entire database records.

This converter handles both component-wise conversion and Unix timestamp binary encoding. Unix timestamps represent seconds elapsed since 1970-01-01T00:00:00Z, requiring 32 bits until the Year 2038 problem forces migration to 64-bit representations. The tool validates against impossible dates (February 30, Month 13) and accounts for leap year rules including the 400-year Gregorian correction. Output includes both raw binary and zero-padded fixed-width formats required by most protocol specifications.

Formulas

Binary conversion applies the division-remainder algorithm. For any decimal integer n, repeatedly divide by 2 and collect remainders in reverse order.

n = k∑i=0 b_i ⋅ 2ⁱ

where b_i ∈ {0, 1} represents each binary digit. The minimum bit width required for value n is:

w = ⌊log₂(n)⌋ + 1

For zero-padded fixed-width output, prepend (W − w) zeros where W is the target width. Unix timestamp conversion first calculates seconds elapsed since the epoch:

t = (Date − 1970-01-01) in seconds

then applies the same base-2 conversion to t. MS-DOS packed date format uses bit fields: 7 bits for year offset from 1980, 4 bits for month, 5 bits for day, concatenated into a 16-bit word.

Reference Data

Date Component	Value Range	Minimum Bits	Standard Width	Binary Example
Day	1 - 31	5 bits	8 bits	00011111 (31)
Month	1 - 12	4 bits	8 bits	00001100 (12)
Year (Short)	0 - 99	7 bits	8 bits	01100011 (99)
Year (Full)	1 - 9999	14 bits	16 bits	0000011111101000 (2024)
Unix Timestamp	0 - 2147483647	31 bits	32 bits	01100101...
Hour	0 - 23	5 bits	8 bits	00010111 (23)
Minute/Second	0 - 59	6 bits	8 bits	00111011 (59)
Week Number	1 - 53	6 bits	8 bits	00110101 (53)
Day of Year	1 - 366	9 bits	16 bits	0000000101101110 (366)
Century	0 - 99	7 bits	8 bits	00010100 (20)
Decade	0 - 9	4 bits	8 bits	00000010 (2)
Quarter	1 - 4	2 bits	8 bits	00000100 (4)
Weekday (ISO)	1 - 7	3 bits	8 bits	00000111 (7)
MS-DOS Date	Packed 16-bit	16 bits	16 bits	YYYYYYYM MMMDDDDD
Julian Day Number	0 - 5373484	23 bits	32 bits	Astronomical dating
Modified Julian	0 - 99999	17 bits	32 bits	Space/telecom standard
Excel Serial Date	1 - 2958465	22 bits	32 bits	Days since 1900-01-01
BCD Date (packed)	6 digits	24 bits	24 bits	YYMMDD in BCD
GPS Week Number	0 - 1023/8191	10/13 bits	16 bits	Weeks since 1980-01-06
TAI64 Label	64-bit	64 bits	64 bits	Seconds since TAI epoch

Frequently Asked Questions

Bit width depends on the numeric value, not digit count. Year 2024 requires 11 bits because 2¹⁰ = 1024 is insufficient while 2¹¹ = 2048 accommodates it. Year 9999 requires 14 bits. Two-digit year representations (00 - 99) fit in 7 bits but introduce Y2K-style ambiguity.

Component-wise conversion produces separate binary values for year, month, and day, preserving human-readable structure. Unix timestamp binary encodes the entire date as a single 32-bit or 64-bit integer representing seconds since 1970-01-01T00:00:00Z. The timestamp approach is more compact but requires conversion to extract date components.

Dates before the Unix epoch produce negative timestamps. In signed 32-bit representation, negative values use two's complement encoding where the most significant bit indicates sign. The converter displays both the signed interpretation and raw bit pattern. Dates before 1901-12-13 overflow signed 32-bit range.

Fixed-width encoding enables direct memory addressing and bit manipulation without parsing overhead. A date stored as three 8-bit values occupies exactly 3 bytes at predictable offsets. Variable-width encoding requires length prefixes or delimiters, complicating real-time processing on microcontrollers with limited instruction sets.

Multiply each bit by its positional power of 2 and sum. For binary 11111101000 (year 2024): 1×1024 + 1×512 + 1×256 + 1×128 + 1×64 + 1×8 = 2024. For fixed-width padded values, leading zeros contribute nothing to the sum.

Signed 32-bit Unix timestamps overflow on 2038-01-19T03:14:07Z when the value exceeds 2147483647. The next second wraps to -2147483648, interpreted as 1901-12-13. Systems must migrate to 64-bit timestamps, which extend the range to approximately 292 billion years.